Every tapered roller bearing front hubs I've tried the north-south shake on has had a play I can feel. I don't think this is a valid test. Maybe your mechanic is used to FWD cars with pre-loaded ball-bearing hubs?

I suggest you follow the advice at this site for proper testing and adjustment.

Steve

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'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7